Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to k-planes with the restriction that their intersection has a prescribed dimension. We study dimensions of restricted secant of Grassmannians and relate them to the analogous question for secants of Grassmannians via an incidence variety construction. We define a notion of expected dimension and give a formula for the dimension of all restricted secant varieties of Grassmannians that holds if the BDdG conjecture [Baur et al. in Exp Math 16(2):239–250, 2007, Conjecture 4.1] on non-defectivity of Grassmannians is true. We also demonstrate example calculations in Macaulay 2, and point out ways to make these calculations more efficient. We also show a potential application to coding theory.

Grassmannians 的受限正割变体由对应于k平面的点的总和构成，并限制它们的交点具有规定的维数。我们研究了 Grassmannians 的受限割线的维度，并通过关联多样性构造将它们与 Grassmannians 割线的类似问题联系起来。我们定义了一个预期维度的概念，并给出了一个公式，用于所有受限制的格拉斯曼割线变体的维度，如果 BDdG 猜想 [Baur 等人。in Exp Math 16(2):239–250, 2007, Conjecture 4.1] 关于 Grassmannians 的非缺陷性是正确的。我们还演示了 Macaulay 2 中的示例计算，并指出了使这些计算更高效的方法。我们还展示了编码理论的潜在应用。